I know I'm going to sound elitist as fuck, but as someone who was quite annoyed with the S5 when it was first revealed (I wanted a more premium designed phone dammit), and switched to several other phones for several days (14 day money back and replacement policy ftw) before ending up settling with the S5 (lol), this is one advantage that cannot be stated enough. Simply put, AMOLED is infinitely superior to all LCD panels on other phones. The black level and contrast performance is just unbelievable really, and to me makes a huge difference to overall media consumption and viewing, especially in dark viewing conditions, where blacks on other devices basically look dark grey. The AMOLED panels on these new devices also no longer have the issues they used to have in older devices, such as a lack of brightness, inaccurate whites, or poorer pixel matrix tech.
It's sort of like comparing my Panasonic VT65 or Pioneer Kuro plasma screens with that of my Macbook Pro Retina or older Sony LCD TV display, the latter just lack the contrast punch and depth, and as a result looks considerably worse. I am dumbfounded that so many sites continue to praise the shit out of the screens on some of these other devices (mobile phones, tablets and laptops alike), because honestly LCD tech, even IPS, still leaves a lot to be desired. And for those worried about saturated colours, or inaccurate levels, Samsung has you covered there as well, with one of the different screen modes that will inevitably be closer to the 6500k standard than even Apple's offerings, but as per usual, many outlets will probably ignore this and harp on with the "over saturated colours and poor white balance" narrative.
I haven't used an Amoled screened phone since my horrible experience with the pentile screen on the Galaxy Nexus. That thing was so fucking ugly to look at, it's a good thing that the tech has come a long way. I'm really looking forward to seeing how it is on the GS6. I always hated the greyish blacks on LCD screens.